CBSE Class 6 Mathematics Chapter 11 Algebra NCERT Solutions

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NCERT Solutions PDF Class 6 PDF

This chapter introduces students to the fundamental concepts of Algebra for Class 6 Mathematics as per NCERT guidelines. It focuses on understanding patterns and forming rules using variables. The solutions cover exercises that require identifying rules for matchstick patterns, applying these rules to real-world scenarios like parades and distributing items, and expressing relationships using variables. Students will learn to represent unknown quantities with letters and form simple algebraic expressions. These solutions provide step-by-step guidance to help students grasp the basics of algebra, build a strong foundation for future mathematical learning, and prepare effectively for exams by understanding how to translate word problems into algebraic expressions.

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Quick info

BoardCBSE
ClassClass 6
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 11

Chapter summary

Chapter 11, Algebra, for Class 6 Mathematics NCERT Solutions, introduces the concept of variables and their use in forming rules for patterns. The solutions focus on identifying and expressing rules for matchstick patterns using algebraic expressions. It also covers applying these algebraic rules to practical situations involving quantities like cadets in a parade, mangoes in boxes, pencils per student, and distance covered by a bird. The exercises emphasize understanding the relationship between quantities and representing them with variables.

Learning outcomes

  • Understand the concept of a variable in algebra.
  • Identify and formulate rules for patterns using variables.
  • Apply algebraic rules to solve real-world problems.
  • Express relationships between quantities using algebraic expressions.
  • Solve problems involving matchstick patterns and their algebraic rules.
  • Relate algebraic expressions to given scenarios.

Topics covered

Paper topics

  • Introduction to Algebra
  • Patterns and Rules
  • Matchstick Patterns
  • Variables
  • Forming Algebraic Expressions
  • Rules for Patterns
  • Algebraic Representation of Quantities
  • Word Problems in Algebra

Important topics

  • Understanding and using variables
  • Formulating rules for matchstick patterns
  • Applying algebraic rules to real-world scenarios
  • Writing algebraic expressions from given information

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Questions and Solutions

Question 1

Find the rule, which gives the number of matchsticks required to make the following matchsticks patterns. Use a variable to write the rule.

(a) A pattern of letter T as

(b) A pattern of letter Z as

(d) A pattern of letter V as

(c) A pattern of letter U as

(e) A pattern of letter E as

(f) A pattern of letter S as

(g) A pattern of letter A as

Solution:

To find the rule for each pattern, we observe how many matchsticks are used to form a single instance of the letter. We then use a variable, typically 'n', to represent the number of times the pattern is repeated. The rule is generally of the form 'constant × n'.

(a) Pattern of letter T: Each 'T' requires 2 matchsticks. So, the rule is 2n.

(b) Pattern of letter Z: Each 'Z' requires 3 matchsticks. So, the rule is 3n.

(c) Pattern of letter U: Each 'U' requires 3 matchsticks. So, the rule is 3n.

(d) Pattern of letter V: Each 'V' requires 2 matchsticks. So, the rule is 2n.

(e) Pattern of letter E: Each 'E' requires 5 matchsticks. So, the rule is 5n.

(f) Pattern of letter S: Each 'S' requires 5 matchsticks. So, the rule is 5n.

(g) Pattern of letter A: Each 'A' requires 6 matchsticks. So, the rule is 6n.

Question 2

We already know the rule for the pattern of letter L, C and F. Some of the letters from Q.1 (given above) give us the same rule as that given by L. Which are these? Why does this happen?
Solution:

The letter 'L' pattern requires 2 matchsticks. From Question 1, we found that the patterns for the letters 'T' and 'V' also use 2 matchsticks each. Therefore, the letters 'T' and 'V' give the same rule (2n) as the letter 'L'. This happens because each of these letters ('L', 'T', and 'V') is constructed using exactly two matchsticks for each instance of the letter in the pattern.

Question 3

Cadets are marching in a parade. There are 5 cadets in a row. What is the rule, which gives the number of cadets, given the number of rows? (Use n for the number of rows)
Solution:

We are given that there are 5 cadets in each row. Let 'n' represent the number of rows in the parade.

Number of rows = n

Number of cadets in each row = 5

To find the total number of cadets, we multiply the number of rows by the number of cadets in each row.

Therefore, the total number of cadets = 5 \times n = 5n.

The rule is 5n.

Question 4

If there are 50 mangoes in a box, how will you write the total number of mangoes in terms of the number of boxes? (Use b for the number of boxes)
Solution:

We know that each box contains 50 mangoes. Let 'b' represent the total number of boxes.

Number of boxes = b

Number of mangoes in each box = 50

To find the total number of mangoes, we multiply the number of boxes by the number of mangoes in each box.

Therefore, the total number of mangoes = 50 \times b = 50b.

The rule is 50b.

Question 5

The teacher distributes 5 pencils per student. Can you tell how many pencils are needed, given the number of students? (Use s for the number of students)
Solution:

The teacher gives 5 pencils to each student. Let 's' represent the total number of students.

Number of students = s

Number of pencils given to each student = 5

To find the total number of pencils needed, we multiply the number of students by the number of pencils each student receives.

Therefore, the total number of pencils needed = 5 \times s = 5s.

The rule is 5s.

Question 6

A bird flies 1 kilometer in one minute. Can you express the distance covered by the bird in terms of its flying time in minutes? (Use t for flying time in minutes)
Solution:

The bird flies at a constant speed. We are given the speed and need to express the distance covered based on the time of flight.

Flying time = t minutes

Speed of the bird = 1 kilometer per minute

The relationship between distance, speed, and time is: Distance = Speed × Time.

Substituting the given values: Distance = 1 \times t km.

Therefore, the distance covered by the bird is t km.

The rule is t.

Common mistakes

  • Confusing variables with constants.
  • Incorrectly forming algebraic rules from patterns.
  • Errors in applying the correct variable to the problem.
  • Misinterpreting the relationship between quantities in word problems.

Revision tips

  • Practice identifying the number of matchsticks needed for each letter pattern.
  • Focus on understanding how a variable represents an unknown or changing quantity.
  • Work through each word problem, clearly defining the variable before writing the rule.
  • Review the relationship between the number of items and the number of groups/rows/students.
  • Ensure you can explain why different patterns might follow the same algebraic rule.

Practice MCQs

Q1. What is the rule for a pattern of the letter 'E' using matchsticks, where 'n' represents the number of letters?

Q2. If there are 'n' rows with 5 cadets in each row, what is the total number of cadets?

Q3. Which of the following letters from Question 1 follows the same rule as the letter 'L' (which uses 2 matchsticks)?

Q4. If a box contains 50 mangoes, and 'b' represents the number of boxes, what is the total number of mangoes?

Q5. A bird flies at a speed of 1 km per minute. If 't' is the flying time in minutes, what is the distance covered?

Frequently asked questions

What is the main concept covered in CBSE Class 6 Maths Chapter 11?

Chapter 11, Algebra, introduces students to the concept of variables and how to use them to form rules for patterns and express relationships between quantities in various scenarios.

How do these NCERT Solutions help students?

These solutions provide clear, step-by-step explanations for each question, helping students understand how to identify patterns, form algebraic rules, and solve problems using variables, which is crucial for exam preparation.

What is a variable in the context of this chapter?

A variable is a symbol, usually a letter like 'n', 'b', or 's', used to represent an unknown or changing quantity. For example, 'n' can represent the number of rows or the number of patterns.

Can you give an example of a rule for a matchstick pattern?

Yes, for a pattern of the letter 'T', which uses 2 matchsticks per letter, the rule is 2n, where 'n' is the number of 'T's in the pattern.

How are algebraic rules applied to real-world problems in this chapter?

The chapter applies algebraic rules to situations like calculating the total number of cadets in a parade based on the number of rows, or the total number of pencils needed based on the number of students.

What is the significance of using variables like 'n', 'b', and 's'?

These variables allow us to write general rules that can be applied to any number of rows, boxes, or students, making the rules flexible and applicable to different situations.

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